Infectious diseases caused by bacteria, fungi, viruses and parasites have affected humans historically. Infectious diseases remain a major cause of premature death and a public health concern globally with increased mortality and significant economic burden. Unvaccinated individuals, people with suppressed and compromised immune systems are at higher risk of suffering from infectious diseases. In spite of significant advancements in infectious diseases research, the control or treatment process faces challenges. The mucosal immune system plays a crucial role in safeguarding the body from harmful pathogens, while being constantly exposed to the environment. To develop treatment options for infectious diseases, it is vital to understand the immune responses that occur during infection. The two infectious diseases presented here are: i) Helicobacter pylori infection and ii) human immunodeficiency (HIV) and human papillomavirus (HPV) co-infection. H pylori, is a bacterium that colonizes the stomach and causes gastric cancer in 1-2% but is beneficial for protection against allergies and gastroesophageal diseases. An estimated 85% of H pylori colonized individuals show no detrimental effects. HIV is a virus that causes AIDS, one of the deadliest and most persistent epidemics. HIV-infected patients are at an increased risk of co-infection with HPV, and report an increased incidence of oral cancer. The goal of this thesis is to elucidate the host immune responses in infectious diseases via the use of computational and mathematical models. First, the thesis reviews the need for computational and mathematical models to study the immune responses in the course of infectious diseases. Second, it presents a novel sensitivity analysis method that identifies important parameters in a hybrid (agent-based/equation-based) model of H. pylori infection. Third, it introduces a novel model representing the HIV/HPV coinfection and compares the simulation results with a clinical study. Fourth, it discusses the need of advanced modeling technologies to achieve a personalized systems wide approach and the challenges that can be encountered in the process. Taken together, the work in this dissertation presents modeling approaches that could lead to the identification of host immune factors in infectious diseases in a predictive and more resource-efficient manner. / Doctor of Philosophy / Infectious diseases caused by bacteria, fungi, viruses and parasites have affected humans historically. Infectious diseases remain a major cause of premature death and a public health concern globally with increased mortality and significant economic burden. These infections can occur either via air, travel to at-risk places, direct person-to-person contact with an infected individual or through water or fecal route. Unvaccinated individuals, individuals with suppressed and compromised immune system such as that in HIV carriers are at higher risk of getting infectious diseases. In spite of significant advancements in infectious diseases research, the control and treatment of these diseases faces numerous challenges. The mucosal immune system plays a crucial role in safeguarding the body from harmful pathogens, while being exposed to the environment, mainly food antigens. To develop treatment options for infectious diseases, it is vital to understand the immune responses that occur during infection. In this work, we focus on gut immune system that acts like an ecosystem comprising of trillions of interacting cells and molecules, including membars of the microbiome. The goal of this dissertation is to develop computational models that can simulate host immune responses in two infectious diseases- i) Helicobacter pylori infection and ii) human immunodeficiency virus (HIV)-human papilloma virus (HPV) co-infection. Firstly, it reviews the various mathematical techniques and systems biology based methods. Second, it introduces a "hybrid" model that combines different mathematical and statistical approaches to study H. pylori infection. Third, it highlights the development of a novel HIV/HPV coinfection model and compares the results from a clinical trial study. Fourth, it discusses the challenges that can be encountered in adapting machine learning based computational technologies. Taken together, the work in this dissertation presents modeling approaches that could lead to the identification of host immune factors in infectious diseases in a predictive and more resourceful way.

Noise reduction in vehicle exhaust systems is crucial for mitigating the adverse health effects of noise from roadside traffic. Improvements to engine exhaust systems could be one avenue to reduce vehicle and roadside noise. Therefore, understanding the insertion loss and transmission loss is of crucial importance as these constitute important metrics for the effectiveness of mufflers in exhaust systems. In addition, knowledge about the maximum emitted sound power is also desirable as it is an important characteristic of the exhaust system affecting the final emitted noise. This study provides an overview of the theoretical underpinnings of the acoustics that model engine exhaust systems, where the maximum sound powers are presented, as well as explores the sensitivity of the insertion and transmission loss to input variables. A sensitivity analysis of the transmission and insertion loss was conducted using data provided by Scania, a large Swedish truck manufacturer, from which it was concluded that the provided transfer matrix exhibit stable behavior. More generally, in face of specific perturbations, if some conditions are meet, the resulting change to the insertion and transmission loss may only be an upwards or downwards translation, or no change at all.

This work is an amalgamation of Theoretical Physics and Applied Mathematics applied on an Epidemiological problem. / Ziel dieser Doktorarbeit ist ein mathematisches Modell zu entwickeln, um eine mögliche Ausbreitung des West-Nil-Virus (WNV) in Deutschland zu simulieren und zu bewerten. Das entwickelte Werkzeug soll auch auf eine weitere, durch Zecken übertragene Krankheit, dem Krim-Kongo-Hämorrhagischen Fieber (CCHFV) angewendet werden. Die durch den Klimawandel verursachte globalen Erwärmung unterstützt auch die Verbreitung und Entwicklung verschiedener Vektorpopulationen. Dabei hat eine Temperaturerhöhung einen positiven Einfluss auf den Lebenszyklus des Vektors und die Zunahme der Vektoraktivität. In dieser Arbeit haben wir ein Differentialgleichungsmodell (ODE) entwickelt, um den Einfluss eines regelmäßigen Eintrags von Infektionserregern auf die empfängliche Population unter Berücksichtigung des Temperatureinflusses zu verstehen. Als Ergebnis haben wir einen analytischen Ausdruck der Basisreproduktionszahl und deren Wechselwirkung mit der Temperatur gefunden. Eine Sensitivitätsanalyse zeigt, wie wichtig das Verhältnis der anfälligen Mücken zur lokalen Wirtspopulation ist. Als ein zentrales Ergebnis haben wir den zukünftigen Temperaturverlauf auf Basis der Modellergebnisse des IPCC in unser Modell integriert und Bedingungen gefunden, unter denen es zu einer dauerhaften Etablierung des West-Nil-Virus in Deutschland kommt. Darüber hinaus haben wir die entwickelten mathematischen Modelle verwendet, um verschiedene Szenarien zu untersuchen, unter denen sich CCHFV möglicherweise in einer naiven Population etablieren kann, und wir haben verschiedene Kontrollszenarien mathematisch abgeleitet, um die Belastung von einer Infektion durch Zecken zu bewältigen. / The objective of this thesis is to develop the necessary mathematical model to assess the potential spread of West Nile Virus (WNV) in Germany and employ the developed tool to analyse another tick-borne disease Crimean- Congo Hemorrhagic Fever (CCHFV). Given the backdrop of global warming and the climate change, increasing temperature has benefitted the vector population. The increase in the temperature has a positive influence in the life cycle of the vector and the increase in its activities. In this thesis, we have developed an Ordinary Differential Equation (ODE) model system to understand the influence of the periodic introduction of infectious agents into the local susceptible population while taking account of influence of temperature. As results, we have found an analytic expression of the basic reproduction number and its interplay with the temperature. The sensitivity analysis shows us the importance of the ratio between the susceptible mosquitoes to the local host population. As a central result we have extrapolated the temperature trend under different IPCC conditions and found the condition under which the circulation of West Nile Virus will be permanent in Germany. Furthermore, we have utilised the developed mathematical models to examine different scenarios under which CCHFV can potentially establish in a naive population along with we mathematically derived different control scenarios to manage the burden of tick infection.

The automotive industry has witnessed a trend in the recent years of reducing the bulk weight of the vehicle in order to achieve improved ride dynamics and economical fuel consumption. Unfortunately, reducing the bulk weight often compromises the noise, vibra- tion, and harshness (NVH) characteristics of the vehicle. In general, the automotive body panels are made out of thin sheet metals (steel and aluminium) that have a very low bend- ing stiffness. Hence, it becomes important to find countermeasures that will increase the structural stiffness of these thin body panels without affecting their bulk weight. One such countermeasure is to introduce the geometrical indentations on various body panels. The geometrical indentation explained in this thesis is in the shape of elliptical dome, which supports the increase of the structural stiffness whilst keeping the bulk weight constant. The primary reason to choose elliptical domes as the applied geometrical indentation is due to a significant amount of interest shown by Jaguar Land Rover. Moreover, the elliptical domes, because of the nature of its design, can cover a larger surface area with minimal depth, thereby, eliminating the possibility of sharp and pointy indentations. This thesis presents a comprehensive study of the structural-acoustic behaviour of the automotive-type panels with dome-shaped indentations. The ultimate aim of this research is to establish a set of design guidelines in order to produce automotive-type panels with optimised dome-shaped indentations. In order to do so, a new design optimisation strategy is proposed that results in the optimal placement of the required dome-shaped indenta- tions. The optimisation problem addressed in this thesis is unlike a general mathematical problem, and requires specific methodologies for its solution. Therefore, the use of genetic algorithm is observed as the most suitable method in order to tackle this type of design optimisation problem. During the development of the optimisation procedure, the preliminary results show a consistency in the design patterns. This led to the motivation to investigate a few intuitively designed panels, which are inspired by the initial, trial, optimisation results. Therefore, four intuitively designed panels are investigated for their structural-acoustic characteristics. The study of the intuitively designed panels provided essential physical insight into the design optimisation problem, which ultimately defined the guidelines in order to develop the proposed optimisation procedure. This type of optimisation procedure is completely new in the domain of structural-acoustic optimisation. The efficiency of the underlying work lies in the separate investigation of both the structural and the acoustic properties of the panels with various dome-shaped indentations, and then utilising the insights gained in order to develop a specific optimisation algorithm to stream-line the dome-shaped panel design procedure.

This thesis deals with chemical plants constituted by parallel batch-continuous production lines with shared resources. For such plants, it is highly desirable to have optimal operation schedules which determine the starting times of the various batch processes and the flow rates of the continuous processes in order to maximize the average plant productivity and to have a continuous production without interruptions. This optimization problem is constrained by the limitation of the resources that are shared by the reactors and by the capacities of the various devices that constitute the plant. Such plants are "hybrid" by nature because they combine both continuous-time dynamics and discrete-event dynamics. The formalism of "Hybrid Automata" is there fore well suited for the design of plant models. The first contribution of this thesis is the development of a hybrid automaton model of the chemical plant in the Matlab-Simulink-Stateflow environment and its use for the design of an optimal periodic schedule that maximises the plant productivity. Using a sensitivity analysis and the concept of Poincaré; map, it is shown that the optimal schedule is a stable limit cycle of the hybrid system that attracts the system trajectories starting in a wide set of initial conditions. The optimal periodic schedule is valid under the assumption that the hybrid model is an exact description of the plant. Under perturbations on the plant parameters, it is shown that two types of problems may arise. The first problem is a drift of the hybrid system trajectory which can either lead to a convergence to a new stable sub-optimal schedule or to a resource conflict. The second problem is a risk of overflow or underflow of the output buffer tank. The second contribution of the thesis is the analysis of feedback control strategies to avoid these problems. For the first problem, a control policy based on a model predictive control (MPC) approach is proposed to avoid resource conflicts. The feedback control is run on - line with the hybrid Simulink-Stateflow simulator used as an internal model. For the solution of the second problem, a classical PI control is used. The goal is not only to avoid over- or under-filling of the tank but also to reduce the amplitude of outflow rate variations as much as possible. A methodological analysis for the PI controller tuning is presented in order to achieve an acceptable trade-off between these conflicting objectives.

本文主要藉由逐次改變二次擔保債權憑證的內層分券金額佔資產池發行金額比例、內層分券下層信用保護金額佔資產池金額比例、資產池參考標的間違約相關性、到期期限、及違約回收率等五項影響二次擔保債權憑證損失發生機率的風險因子，結合蒙地卡羅模擬法及關聯結構法模擬交易架構中內層、外層分券不同損失率的發生機率，並利用彈性分析，衡量二次擔保債券憑證在每單位風險因子變動下，內層及外層分券的損失發生機率。 研究結果顯示，相同的風險因子對於內層與外層分券的損失發生機率的影響效果並不相同，此一現象有別於一般認為風險因子對內、外層分券損失發生機率影響效果相同的看法。此外，依據分券損失發生機率對每單位風險因子變化的彈性敏感性分析，分券損失發生機率受風險因子的影響可分為: 彈性為正且數值逐漸增加、彈性為正且逐漸下降、彈性為負且數值 (絕對值) 逐漸下降、及彈性為負且數值 (絕對值) 逐漸增加四類。外層夾層分券的損失發生機率對內層分券厚度占資產池金額比例的彈性為負，其數值 (絕對值) 隨著內層分券厚度占資產池金額比例的增加而下降。外層夾層分券的損失發生機率對內層分券下層信用保護金額佔資產池金額比例的彈性、及外層夾層分券的損失發生機率對參考標的違約回收率的彈性為負，且數值 (絕對值) 隨著下層信用保護比例及回收率的增加而上升。外層夾層分券的損失發生機率對參考標的違約相關係數的彈性為正，其數值隨著相關係數的增加而下降；外層夾層分券的損失發生機率對參考標的之到期期限的彈性為正，其數值隨著到期期限的增加而上升。 / The researchers of this study combined Monte Carlo simulation approach and copula method to change the following five risk factors: the thickness of inner CDOs tranche on CDO-squared, the subordination in master CDOs tranche, the correlation of reference entities, the maturity of reference entities, and the recovery rate of reference entities, with a purpose of simulating the loss possibility of CDOs-squared. Besides, by elasticity analysis, the researchers measured the change of loss rate according to the change of each risk factor per unit. The result of the study shows that the same risk factor has different influence on the loss rate of inner and master tranche of CDOs squared, which mismatches the general belief that the same risk factor has the same effect on the loss rate of inner and master CDOs tranche. In addition, according to the tranche loss possibility elasticity analysis to the risk factors, this research reveals that four categories can be made due to the effect which risk factors have on loss rate : positive and increasing elasticity, positive and decreasing elasticity, negative and increasing elasticity, and negative decreasing elasticity. We found that for the master mezzanine tranche: the elasticity of tranche loss possibility to the thickness of inner CDOs tranche of CDO-squared is negative and will decrease with the increasing thickness of inner CDOs tranche. The elasticity of tranche loss possibility to subordination in inner CDOs tranche and the elasticity of tranche loss possibility to the recovery rate of reference entities are both negative and will increase with the increasing subordination of inner CDOs tranche and the recovery rate of reference entities. The elasticity of the loss rate possibilities to the correlation of reference entities default is positive and will decrease with the increasing correlation of reference entities. The elasticity of loss possibilities to the maturity of reference entities is positive and will increase with the increasing maturity.

This study was based on the uncertainty and sensitivity analysis of a generic 10 MW Materials Test Reactor (MTR). In this study an uncertainty and sensitivity analysis methodology called code scaling applicability and uncertainty (CSAU) was implemented. Although this methodology follows 14 steps, only the following were carried out: scenario specification, nuclear power plant (NPP) selection, phenomena identification and ranking table (PIRT), selection of frozen code, provision of code documentation, determination of code applicability, determination of code and experiment accuracy, NPP sensitivity analysis calculations, combination of biases and uncertainties, and total uncertainty to calculate specific scenario in a specific NPP. The thermal hydraulic code Flownex®1 was used to model only the reactor core to investigate the effects of the input parameters on the selected output parameters of the hot channel in the core. These output parameters were mass flow rate, temperature of the coolant, outlet pressure, centreline temperature of the fuel and surface temperature of the cladding. The PIRT process was used in conjunction with the sensitivity analysis results in order to select the relevant input parameters that significantly influenced the selected output parameters. The input parameters that have the largest effect on the selected output parameters were found to be the coolant flow channel width between the plates in the hot channel, the width of the fuel plates itself in the hot channel, the heat generation in the fuel plate of the hot channel, the global mass flow rate, the global coolant inlet temperature, the coolant flow channel width between the plates in the cold channel, and the width of the fuel plates in the cold channel. The uncertainty of input parameters was then propagated in Flownex using the Monte Carlo based uncertainty analysis function. From these results, the corresponding probability density function (PDF) of each selected output parameter was constructed. These functions were found to follow a normal distribution. / MIng (Nuclear Engineering), North-West University, Potchefstroom Campus, 2014

Starting with the development of an enzymatic assay, where an enzyme in solution hydrolysed a solid-phase bound peptide, a model for the kinetics of enzyme action was introduced. This model allowed the estimation of kinetic parameters and enzyme activity for a system that has the peculiarity of not being saturable with the substrate, but with the enzyme. In a derivation of the model, it was found that the sensitivity of the signal to variations in the enzyme concentration had a transient increase along the reaction progress with a maximum at high substrate conversion levels. The same behaviour was derived for the sensitivity in classical homogeneous enzymatic assays and experimental evidence of this was obtained. The impact of the transient increase of the sensitivity on the error structure, and on the ability of homogeneous end-point enzymatic assays to detect competitive inhibition, came into focus. First, a non-monotonous shape in the standard deviation of progress curve data was found and it was attributed to the random dispersion in the enzyme concentration operating through the transient increase in the sensitivity. Second, a model for the detection limit of the quantity Ki/[I] (the IDL-factor) as a function of the substrate conversion level was developed for homogeneous end-point enzymatic assays. It was found that the substrate conversion level where the IDL-factor reached an optimum was beyond the initial velocity range. Moreover, at this optimal point not only the ability to detect inhibitors but also the robustness of the assays was maximized. These results may prove to be relevant in drug discovery for optimising end point homogeneous enzymatic assays that are used to find inhibitors against a target enzyme in compound libraries, which are usually big (>10000) and crowded with irrelevant compounds.

In this thesis we develop methods for dealing with missing data in a univariate response variable when estimating regression parameters. Missing outcome data is a problem in a number of applications, one of which is follow-up studies. In follow-up studies data is collected at two (or more) occasions, and it is common that only some of the initial participants return at the second occasion. This is the case in Paper II, where we investigate predictors of decline in self reported health in older populations in Sweden, the Netherlands and Italy. In that study, around 50% of the study participants drop out. It is common that researchers rely on the assumption that the missingness is independent of the outcome given some observed covariates. This assumption is called data missing at random (MAR) or ignorable missingness mechanism. However, MAR cannot be tested from the data, and if it does not hold, the estimators based on this assumption are biased. In the study of Paper II, we suspect that some of the individuals drop out due to bad health. If this is the case the data is not MAR. One alternative to MAR, which we pursue, is to incorporate the uncertainty due to missing data into interval estimates instead of point estimates and uncertainty intervals instead of confidence intervals. An uncertainty interval is the analog of a confidence interval but wider due to a relaxation of assumptions on the missing data. These intervals can be used to visualize the consequences deviations from MAR have on the conclusions of the study. That is, they can be used to perform a sensitivity analysis of MAR. The thesis covers different types of linear regression. In Paper I and III we have a continuous outcome, in Paper II a binary outcome, and in Paper IV we allow for mixed effects with a continuous outcome. In Paper III we estimate the effect of a treatment, which can be seen as an example of missing outcome data.

Malfunction of the system which regulates the bloodflow in the brain is a major cause of stroke and dementia, costing many lives and many billions of pounds each year in the UK alone. This regulatory system, known as cerebral autoregulation, has been the subject of much experimental and mathematical investigation yet our understanding of it is still quite limited. One area in which our understanding is particularly lacking is that of the role of nitric oxide, understood to be a potent vasodilator. The interactions of nitric oxide with the better understood myogenic response remain un-modelled and poorly understood. In this thesis we present a novel model of the arteriolar control mechanism, comprising a mixture of well-established and new models of individual processes, brought together for the first time. We show that this model is capable of reproducing experimentally observed behaviour very closely and go on to investigate its stability in the context of the vasculature of the whole brain. In conclusion we find that nitric oxide, although it plays a central role in determining equilibrium vessel radius, is unimportant to the dynamics of the system and its responses to variation in arterial blood pressure. We also find that the stability of the system is very sensitive to the dynamics of Ca²⁺ within the muscle cell, and that self-sustaining Ca2+ waves are not necessary to cause whole-vessel radius oscillations consistent with vasomotion.